Find change in internal energy of gas if its temperature changes by 10K. Number of moles of gas is 10. C_P (specific heat at constant pressure of the gas) is 7 cal/K-mol and R (gas constant) = 2 cal/K.

The correct answer is 500 cal.

To find the change in the internal energy of the gas, we can use the relationship between the change in internal energy, the number of moles, the molar specific heat capacity at constant volume, and the change in temperature.

1. Identify the given parameters:
Number of moles ($n$) = 10
Change in temperature ($\Delta T$) = 10 K
Molar specific heat capacity at constant pressure ($C_p$) = 7 cal/K-mol
Universal gas constant ($R$) = 2 cal/K-mol

2. Find the molar specific heat capacity at constant volume ($C_v$):
According to Mayer's relation for an ideal gas:
$C_p-C_v=R$
Rearranging the formula to solve for $C_v$:
$C_v=C_p-R$
Substituting the given values:
$C_v=7-2=5\text{cal/K-mol}$

3. Calculate the change in internal energy ($\Delta U$):
The change in internal energy is given by:
$\Delta U=n{C}_v\Delta T$
Substituting the values into the formula:
$\Delta U=10\times 5\times 10$
$\Delta U=500\text{cal}$

Thus, the change in the internal energy of the gas is 500 cal.