5 moles of an unknown gas are heated at constant volume from 10°C to 20°C. The molar specific heat at constant pressure is:

C_p = 8 cal mol^-1 °C^-1

Gas constant:

R = 8.36 J mol^-1 K^-1

Find the change in internal energy of the gas.

At constant volume, the change in internal energy is:

ΔU = nC_vΔT

We are given C_p, therefore first calculate C_v.

For an ideal gas:

C_p − C_v = R

Convert R into calories:

R = 8.36 / 4.18

= 2 cal mol^-1 K^-1

Therefore:

C_v = 8 − 2

= 6 cal mol^-1 K^-1

Temperature rise:

ΔT = 20 − 10

= 10°C

Substituting values:

ΔU = 5 × 6 × 10

= 300 cal

Final Answer

300 cal