Question

1. a 360 - g insulated metal container holds 180.0 g of water, both initially at 22.0°c. when a 24.0 - g ice cube, at the melting point, is dropped into the water, the final temperature reaches 15.0°c. assume no heat is exchanged with the surroundings. for water, the specific heat capacity is 4186 j/kg·°c and the latent heat of fusion is 3.34×105 j/kg. what is the specific heat capacity of the metal container?

a. 970 j/kg·°c
b. 1686 j/kg·°c
c. 3300 j/kg·°c
d. 2300 j/kg·°c

1. what does latent heat refer to?

a. heat that changes temperature
b. heat lost during cooling
c. heat required for a phase change.
d. heat required during heating

1. during an adiabatic compression, 200 j of work is applied to a gas. what is the resulting change in the internal energy of the gas in this process?

a. 0 j
b. 100 j
c. 200 j
d. - 200 j

Explanation:

Question 4

Step1: Calculate heat gained by ice

The ice melts (latent heat) and then warms.
For melting: \(Q_1 = m_{ice}L_f\), \(m_{ice}=24.0\ g = 0.024\ kg\), \(L_f = 3.34\times10^5\ J/kg\), so \(Q_1=0.024\times3.34\times 10^5=8016\ J\)
For warming: \(Q_2=m_{ice}c_{water}(T - T_{melt})\), \(T_{melt}=0^{\circ}C\), \(T = 15^{\circ}C\), \(m_{ice}=0.024\ kg\), \(c_{water}=4186\ J/kg\cdot^{\circ}C\), so \(Q_2=0.024\times4186\times15 = 1506.96\ J\)
Total heat gained by ice \(Q_{ice}=Q_1 + Q_2=8016+1506.96 = 9522.96\ J\)

Step2: Calculate heat lost by water and container

Heat lost by water: \(Q_{water}=m_{water}c_{water}(T_{initial}-T)\), \(m_{water}=0.18\ kg\), \(T_{initial}=22^{\circ}C\), \(T = 15^{\circ}C\), \(c_{water}=4186\ J/kg\cdot^{\circ}C\), so \(Q_{water}=0.18\times4186\times(22 - 15)=5274.36\ J\)
Let \(c\) be the specific heat capacity of the container. Heat lost by container: \(Q_{container}=m_{container}c(T_{initial}-T)\), \(m_{container}=0.36\ kg\), \(T_{initial}=22^{\circ}C\), \(T = 15^{\circ}C\)
By heat - balance \(Q_{ice}=Q_{water}+Q_{container}\)
\(9522.96=5274.36+0.36\times c\times(22 - 15)\)
\(0.36\times c\times7=9522.96 - 5274.36\)
\(2.52c = 4248.6\)
\(c=\frac{4248.6}{2.52}=1686\ J/kg\cdot^{\circ}C\)

Latent heat is the heat required for a phase change (e.g., melting, boiling) without a change in temperature. Heat that changes temperature is related to specific heat (\(Q = mc\Delta T\)). Heat lost during cooling and heat required during heating (in the context of just temperature change) are not latent heat.

For an adiabatic process, \(Q = 0\). From the first law of thermodynamics \(\Delta U=Q + W\). Given \(W = 200\ J\) (work done on the gas, so positive) and \(Q = 0\), then \(\Delta U=W\)

Answer:

B. \(1686\ J/kg\cdot^{\circ}C\)

Question 5