To raise the temperature of 2 mole of an ideal gas from 30^ C to 35^ C at constant pressure, 70 calories of heat is required. The amount of heat needed to raise the temperature of the same gas across the same range at constant volume is

Step-by-step solution

Given n = 2 , T = 35^ C - 30^ C = 5 K , and Q_p = 70 cal . The heat required at constant pressure is given by: Q_p = n C_p T 70 = 2 C_p 5 C_p = 7 cal mol ⁻¹ K ⁻¹ Using the relation C_p - C_v = R and taking R 2 cal mol ⁻¹ K ⁻¹ : C_v = 7 - 2 = 5 cal mol ⁻¹ K ⁻¹ The heat required at constant volume is: Q_v = n C_v T Q_v = 2 5 5 = 50 cal