The molar heat capacity for an ideal gas at constant pressure is 20.785 J K–1 mol–1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is _____. (Nearest integer)
(Given : R = 8.314 JK-1mol-1).
(Given : R = 8.314 JK-1mol-1).
Correct Answer: 2
Solution and Explanation
Cp = 20.785 JK-1 mol-1 and ΔU = nCvΔT
∴ nCv = \(\frac{5000}{200}\) = 25
and we know that
Cp – Cv = R
20.785\(-\frac{25}{n} \)= 8.314
n = \(\frac{25}{(20.785-8.314)}\)
= 2
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Concepts Used:
Specific Heat Capacity
Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
Molar Specific Heat:
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
Specific Heat at Constant Pressure or Volume:
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.