If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, what is the change in internal energy of a mass of gas when the volume changes from V t... If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, what is the change in internal energy of a mass of gas when the volume changes from V to 2V under constant pressure p? Read more

Steps to Solve

1. Identify the Formula
   To find the change in internal energy ($\Delta U$) of a gas at constant pressure, we use the first law of thermodynamics. The formula is:
   $$ \Delta U = Q - W $$
   Where $Q$ is the heat added to the system and $W$ is the work done by the system.

2. Calculate Work Done
   At constant pressure, the work done by the gas when it expands or contracts is given by the formula:
   $$ W = P \Delta V $$
   Where $P$ is the pressure and $\Delta V$ is the change in volume.

3. Calculate Heat Added
   For an ideal gas at constant pressure, the heat added can be calculated using the specific heat capacity at constant pressure ($C_p$) and the change in temperature ($\Delta T$):
   $$ Q = n C_p \Delta T $$
   Where $n$ is the number of moles of gas.

4. Combine the Equations
   Substituting the expressions for $Q$ and $W$ into the first law of thermodynamics gives us:
   $$ \Delta U = n C_p \Delta T - P \Delta V $$

5. Final Expression
   Depending on the problem specifics, values for $n$, $C_p$, $\Delta T$, $P$, and $\Delta V$ can then be substituted into the equation to find $\Delta U$.