A rigid container holds 20 g of a gas. When heat is supplied to the gas, its internal energy increases by 418 J . If the specific heat capacity of the gas at constant volume is 0.25 cal g ⁻¹ ^ C ⁻¹ and 1 cal = 4.18 J , the rise in temperature of the gas is:

Step-by-step solution

For a gas in a rigid container, the volume is constant (isochoric process). Thus, the work done is zero and the change in internal energy is given by: U = m c_v T Given: U = 418 J m = 20 g c_v = 0.25 cal g ⁻¹ ^ C ⁻¹ = 0.25 4.18 J g ⁻¹ ^ C ⁻¹ = 1.045 J g ⁻¹ ^ C ⁻¹ Substituting the values: 418 = 20 1.045 T 418 = 20.9 T T = 418 20.9 = 20^ C Answer: 20^ C