GRE Subject Test: Chemistry : General Thermodynamics

Study concepts, example questions & explanations for GRE Subject Test: Chemistry

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Example Questions

Example Question #1 : Heat And Temperature

Calculate the final temperature when a \displaystyle 44.0g sample of metal (specific heat of the metal=\displaystyle 0.52 \frac{J}{g^{o}C}) at \displaystyle 45.0^{o}C is placed into \displaystyle 95.0g of water at \displaystyle 23.0^{o}C. (specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C})

Possible Answers:

\displaystyle 132^{o}C

\displaystyle 76^{o}C

\displaystyle 17^{o}C

\displaystyle 24^{o}C

Correct answer:

\displaystyle 24^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(44.0g\cdot 0.52\frac{J}{g^{o}C}\cdot (T_{f}-45.0^oC)=95.0g\cdot4.18\frac{J}{g^o}C(T_{f}-23^{o}C)

\displaystyle -(22.9\frac{J}{^{o}C}(T_{f}-45.0^{o}C))=397\frac{J}{^{o}C}(T_{f}-23^{o}C)

\displaystyle -(22.9\frac{J}{^{o}C}\cdot T_{f}-22.9\frac{J}{^{o}C}\cdot 45.0^{o}C)=397\frac{J}{^{o}C}\cdot T_{f}-397\frac{J}{^{o}C}\cdot 23.0^{o}C

\displaystyle -(22.9\frac{J}{^{o}C}\cdot T_{f}-1031J)=397\frac{J}{^{o}C}\cdot T_{f}-9131J

\displaystyle -22.9\frac{J}{^{o}C}\cdot \ T_{f}+1031J=397\frac{J}{^{o}C}\cdot T_{f}-9131J

\displaystyle -22.9\frac{J}{^{o}C}\cdot \ T_{f}-397\frac{J}{^{o}C}\cdot T_{f}=-1031J-9131J

\displaystyle -419\frac{J}{^{o}C}\cdot T_{f}=-10162J

\displaystyle T_{f}=\frac{-10162^{o}C}{-419.9}=24^{o}C

 

Example Question #1 : Heat And Temperature

Calculate the specific heat of \displaystyle 19.3 g of metal that requires \displaystyle 353 J of heat energy to raise its temperature from \displaystyle 17.0^{o}C to \displaystyle 44.0^{o}C?

Possible Answers:

\displaystyle 0.677\frac{J}{g^{o}C}

\displaystyle 17\frac{J}{g^{o}C}

\displaystyle 0.581\frac{J}{g^{o}C}

\displaystyle 0.98\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.677\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

\displaystyle C=\frac{Q}{m\bigtriangleup T}=\frac{353J}{(19.3g\times (44.0^{o}C-17.0^{o}C))}=0.677\frac{J}{g^{o}C}

Example Question #31 : Thermodynamics And Phases

What was the final temperature of the water if a \displaystyle 33.0 g sample of water absorbs \displaystyle 423 J of heat energy and heats up from \displaystyle 23^{o}C? (specific heat of water is \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 71^{o}C

\displaystyle 54^{o}C

\displaystyle 28^{o}C

\displaystyle 117^{o}C

Correct answer:

\displaystyle 28^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Rearranging gives,

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle 423J=19g\times4.18\frac{J}{g^{o}C}\times(T_{f}-23^{o}C)

\displaystyle 423J=79\frac{J}{^{o}C}\times(T_{f}-23^{o}C)

\displaystyle \frac{423J}{79\frac{J}{^{o}C}}=T_{f}-23^{o}C

\displaystyle 5.35^{o}C=T_{f}-23^{o}C

\displaystyle T_{f}=28^{o}C

Example Question #41 : Physical Chemistry

A \displaystyle 20.5 g metal at \displaystyle 37.1^{o}C was placed in \displaystyle 23.3 g of water at \displaystyle 24.2^{o}C. The final temp of the water and metal was \displaystyle 26.0^{o}C. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C}.

Possible Answers:

\displaystyle 0.897\frac{J}{g^{o}C}

\displaystyle 2.32\frac{J}{g^{o}C}

\displaystyle 1.2\frac{J}{g^{o}C}

\displaystyle 0.77\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.77\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(20.5g\cdot C\cdot (26.0^{o}C-37.1^oC)=23.3g\cdot4.18\frac{J}{g^o}C(26.0^{o}C-24.2^{o}C)

\displaystyle -(-227.55g^{o}C\cdot C)=175.3092J

\displaystyle 227.55g^{o}C\cdot\ C=175.3092J

\displaystyle C=\frac{175.3092J}{227.55g^{o}C}=0.77\frac{J}{g^{o}C}

Example Question #361 : Gre Subject Test: Chemistry

What was the final temperature of the water if a \displaystyle 112 g sample of water absorbs \displaystyle 231 J of heat energy and heats up from \displaystyle 25.0^{o}C? (specific heat of water= \displaystyle 4.18\frac{J}{g^{o}C})

Possible Answers:

\displaystyle 134^{o}C

\displaystyle 25.5^{o}C

\displaystyle 43.2^{o}C

\displaystyle 75^{o}C

Correct answer:

\displaystyle 25.5^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Rearranging gives,

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle 231J=112g\times4.18\frac{J}{g^{o}C}\times(T_{f}-25.0^{o}C)

\displaystyle 231J=468.16\frac{J}{^{o}C}\times(T_{f}-25.0^{o}C)

\displaystyle \frac{231J}{468.16\frac{J}{^{o}C}}=T_{f}-25.0^{o}C

\displaystyle 0.493^{o}C=T_{f}-25.0^{o}C

\displaystyle T_{f}=25.5^{o}C

Example Question #1 : Heat And Temperature

A \displaystyle 10.2 g metal at \displaystyle 72.9^{o}C was placed in \displaystyle 21.2 g of water at \displaystyle 25.0^{o}C. The final temp of the water and metal was \displaystyle 53.3^{o}C. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C}.

Possible Answers:

\displaystyle 465\frac{J}{g^{o}C}

\displaystyle 12.5\frac{J}{g^{o}C}

\displaystyle 2.6\frac{J}{g^{o}C}

\displaystyle 173\frac{J}{g^{o}C}

Correct answer:

\displaystyle 12.5\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(10.2g\cdot C\cdot (53.3^{o}C-72.9^oC)=21.2g\cdot4.18\frac{J}{g^o}C(53.3^{o}C-25.0^{o}C)

\displaystyle -(-199.92g^{o}C\cdot C)=2507.83J

\displaystyle 199.92g^{o}C\cdot C=2507.83J

\displaystyle C=\frac{2507.83J}{199.92g^{o}C}=12.5\frac{J}{g^{o}C}

Example Question #361 : Gre Subject Test: Chemistry

How much heat is absorbed when \displaystyle 150 g of water goes from \displaystyle 25.0^{o}C to \displaystyle 35.0^{o}C? (Specific heat of water= \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 6270\ J

\displaystyle 2270\ J

\displaystyle 12\ J

\displaystyle 70\ J

Correct answer:

\displaystyle 6270\ J

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle Q=150g\cdot\ 4.18\frac{J}{g^{o}C}\cdot (35^{o}C-25^{o}C)

\displaystyle Q=6270\ J

Example Question #11 : General Thermodynamics

Calculate the specific heat of  \displaystyle 20.4 g of metal that requires \displaystyle 410.4 J of heat energy to raise its temperature from \displaystyle 20.46^{o}C to \displaystyle 64.4^{o}C

Possible Answers:

\displaystyle 0.21\frac{J}{g^{o}C}

\displaystyle 4.2\frac{J}{g^{o}C}

\displaystyle 1.6\frac{J}{g^{o}C}

\displaystyle 0.516\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.516\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

 

\displaystyle C=\frac{Q}{m\bigtriangleup T}=\frac{410.4J}{(20.4g\times (64.4^{o}C-25.4^{o}C))}=0.516\frac{J}{g^{o}C}

Example Question #42 : Physical Chemistry

Calculate the final temperature when a \displaystyle 14.7g sample of metal (specific heat of the metal=\displaystyle 0.72 \frac{J}{g^{o}C}) at \displaystyle 37.0^{o}C is placed into \displaystyle 31.7g of water at \displaystyle 26.2^{o}C. (Specific heat of water is \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 36^oC

\displaystyle 18^oC

\displaystyle 54^oC

\displaystyle 27^oC

Correct answer:

\displaystyle 27^oC

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(14.7g\cdot 0.72\frac{J}{g^{o}C}\cdot (T_{f}-37.0^oC)=31.7g\cdot4.18\frac{J}{g^o}C(T_{f}-26.2^{o}C)

\displaystyle -(10.584\frac{J}{^{o}C}(T_{f}-37.0^{o}C))=132.51\frac{J}{^{o}C}(T_{f}-26.2^{o}C)

\displaystyle -(10.584\frac{J}{^{o}C}\cdot T_{f}-10.584\frac{J}{^{o}C}\cdot 37.0^{o}C)=132.51\frac{J}{^{o}C}\cdot T_{f}-132.51\frac{J}{^{o}C}\cdot 26.2^{o}C

\displaystyle -(10.584\frac{J}{^{o}C}\cdot T_{f}-391.61J)=132.51\frac{J}{^{o}C}\cdot T_{f}-3472J

\displaystyle -10.584\frac{J}{^{o}C}\cdot T_{f}+391.61J=132.51\frac{J}{^{o}C}\cdot T_{f}-3472J

\displaystyle -10.584\frac{J}{^{o}C}\cdot T_{f}-132.51\frac{J}{^{o}C}\cdot T_{f}=-3472J-391.61J

\displaystyle -143.094\frac{J}{^{o}C}\cdot T_{f}=-3863.61J

\displaystyle T_{f}=\frac{-3863.61^{o}C}{-143.094}=27^{o}C

Example Question #43 : Physical Chemistry

How much heat is absorbed when \displaystyle 50 g of water goes from \displaystyle 24.5^{o}C to \displaystyle 43.0^{o}C? (Specific heat of water = \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 896J

\displaystyle 43J

\displaystyle 166J

\displaystyle 3867J

Correct answer:

\displaystyle 3867J

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Rearranging gives,

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle Q=50g\cdot\ 4.18\frac{J}{g^{o}C}\cdot (43.0^{o}C-24.5^{o}C)

\displaystyle Q=3867\ J

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