The heat capacity of an object indicates how much energy that object can absorb
ID: 517824 • Letter: T
Question
The heat capacity of an object indicates how much energy that object can absorb for a given increase in that object's temperature. In a system in which two objects of different temperatures come into contact with one another, the warmer object will cool and the cooler object will warm up until the system is at a single equilibrium temperature.
Note the difference between the terms molar heat capacity, which has units of J/(molC), and specific heat, which has units of J/(gC).
In this problem answers are requested to three significant digits for grading purposes. The true number of significant digits may be more or less.
Part A
Use the following values:
specific heat of water = 4.18 J/(gC)
specific heat of steel = 0.452 J/(gC)
Express your answer to three significant figures and include the appropriate units.
SubmitHintsMy AnswersGive UpReview Part
The heat capacity of an object indicates how much energy that object can absorb for a given increase in that object's temperature. In a system in which two objects of different temperatures come into contact with one another, the warmer object will cool and the cooler object will warm up until the system is at a single equilibrium temperature.
Note the difference between the terms molar heat capacity, which has units of J/(molC), and specific heat, which has units of J/(gC).
In this problem answers are requested to three significant digits for grading purposes. The true number of significant digits may be more or less.
Part A
A volume of 120. mL of H2O is initially at room temperature (22.00 C). A chilled steel rod at 2.00 C is placed in the water. If the final temperature of the system is 21.50 C , what is the mass of the steel bar?Use the following values:
specific heat of water = 4.18 J/(gC)
specific heat of steel = 0.452 J/(gC)
Express your answer to three significant figures and include the appropriate units.
mass of the steel =SubmitHintsMy AnswersGive UpReview Part
Explanation / Answer
1)As there is no special note that we assume that there is no heat exchange with the environment. In such case, the amount of heat taken by the steel rod (Qs) is equal to the amount of heat lost
by water (Qw) but with opposite sign:
Qs = -Qw.
In future formulas, all values related to water will have index w and those for the steel rod will have index s.
2) Let’s write the generic expression connecting amount of heat (Q), the temperature change of the object (T-T0), where T0– initial temperature of the object, T –final temperature of the object),
specific heat (C) and the mass of the object (m):
Q = C*(T-T0)*m
3) Let’s write condition from 1) using expression from 2):
Cs*(Ts-T0s)*ms = - Cw*(Tw-T0w)*mw.
4) Derive mass of steel rod from 3):
ms = - Cw*(Tw-T0w)*mw / (Cs*(Ts-T0s))
Note, that the mass of the water = volume of water * density of water = 120 mL * 1.00 g/mL =
120.00 g.
5)Calculate:
ms = - 4.18 J/(g oC) * (21.5 oC – 22.00 oC) * 120.00 g / (0.452 J/(g oC) /* (21.5 oC – 2.00 oC))
= 28.454 g.
Answer:
The mass of the steel bar is 28.5 g (three significant figures)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.