For one mole of an ideal gas, the amount of heat required to raise its temperature by 1 K at constant volume is x . The amount of heat required to raise the temperature of the same gas by 1 K at constant pressure will be (where R is the universal gas constant):

Step-by-step solution

The heat required to raise the temperature of n moles of an ideal gas by T at constant volume is given by Q_V = n C_V T . Given n = 1 mol and T = 1 K , we have Q_V = C_V = x . The heat required to raise the temperature of the gas by T at constant pressure is given by Q_P = n C_P T . For n = 1 mol and T = 1 K , we have Q_P = C_P . Using Mayer's relation for an ideal gas, C_P - C_V = R . Substituting C_V = x , we get C_P = x + R . Therefore, the amount of heat required at constant pressure is x + R . Answer: x + R