# Molar specific heat

## Homework Statement

(a) Steam coming from a geyser at 100°C expands as it rises into the air. Since this expansion is rapid over the first small time interval we can assume that this occurs with no heat loss to the surrounding air in the region of the vent. What happens to the temperature when its initial volume is increased to four times its initial volume?

(b) The ratio of Cp/Cv for a particular gas is 1.65. What are the types of energy that are contributing to the molar specific heat? Choose one of the following:

· translation only

· translation and rotation only

· translation, rotation and vibration

· translation and vibration only

## The Attempt at a Solution

(a) I tried this equation

$$T_iV_i^{\gamma-1}=T_fV_f^{\gamma-1}$$

100°C = 373.15 K. Also the theoretical value for $$\gamma$$ is

$$\gamma= \frac{C_p}{C_V}=\frac{5R/2}{3R/2}= \frac{5}{3}=1.67$$

$$(373.15 K) =T_f (4^{0.67})$$

Tf=147.40 K

Why is my answer not correct?

(b) I don't know how to decide what types of energy are contributing to the molar specific heat. I know that the ratio of molar specefic heat is equal to 1.67 and the ratio of the particular gas given is in good adreement with this experimental values obtained for monatomic gases. But I don't know how to determine if the types of energy that are contributing to the molar specific heat are rotational/viberational/rotational. Any explanation is appreciated.

Okay I figured out part (b) but I still don't know why I get part (a) wrong!

I used the equation that gives the relationship between T and V for an adiabatic process involving an ideal gas:

$$T_iV_i^{\gamma -1}=T_fV_f^{\gamma -1}$$

$$373.15 K = T_f 4^{0.67}$$

$$T_f=147.40$$

But this does not agree with the model answer (235.0 K). Is there something wrong with my method?