Heat capacities and their relations

36 questions on Heat capacities and their relations from the Thermodynamics and Thermochemistry chapter: 8 NEET level, 14 JEE Main, 14 JEE Advanced. Each one opens with its answer and solution.

• For one mole of an ideal gas, C_P - C_V equals NEET level
• The ratio gamma = C_P/C_V for an ideal monatomic gas is NEET level
• At ordinary temperatures, where vibrations are not excited, the molar heat capacity at constant volume of a diatomic ideal gas is NEET level
• Heat required to raise the temperature of 2 mol of a monatomic ideal gas by 10 K at constant volume (R = 8.314 J mol^-1K^-1) is NEET level
• One mole of a diatomic ideal gas (no vibrational contribution) is heated at constant pressure from 300 K to 420 K. With R = 8.314 J mol^-1K^-1, the change in in... JEE Main level
• An ideal gas with gamma = C_P/C_V = 1.40 absorbs 1.90 kJ of heat per mole at constant pressure. With R = 8.314 J mol^-1K^-1, the temperature rise of one mole is... JEE Main level
• A monatomic ideal gas initially at 300 K is compressed reversibly and adiabatically to half its volume. The final temperature is closest to JEE Main level
• Which of the following statements about ideal gases is/are correct? JEE Main level
• A 50.0 g piece of metal at 100.0 degC is dropped into 100.0 g of water at 20.0 degC in an insulated container; the final temperature is 26.0 degC. Take c(water)... JEE Main level
• Two moles of a diatomic ideal gas (vibrations ignored) cool from 400 K to 300 K by a reversible adiabatic expansion. With R = 8.314 J mol^-1K^-1, the work done ... JEE Main level
• The molar heat capacity at constant pressure of a certain ideal gas is 37.1 J mol^-1K^-1. Using R = 8.314 J mol^-1K^-1, the ratio gamma = C_P/C_V is closest to JEE Main level
• For N2(g) + 3H2(g) -> 2NH3(g), Delta H deg_298 = -92.2 kJ. Molar heat capacities C_P (assumed constant, J mol^-1K^-1): N2 29.1, H2 28.8, NH3 35.1. Using Kirchho... JEE Advanced level
• A gas mixture contains 1.00 mol He and 2.00 mol O2 (treat O2 as a rigid diatomic ideal gas with vibrations frozen; R = 8.314 J mol^-1K^-1). Which statements are... JEE Advanced level
• Two moles of a monatomic ideal gas at 450 K and 10.0 L expand reversibly and adiabatically to 40.0 L. With R = 8.314 J mol^-1K^-1, the magnitude of work done by... JEE Advanced level
• One mole of a monatomic ideal gas at 300 K and 4.0 atm expands adiabatically against a constant external pressure of 1.0 atm until it reaches mechanical equilib... JEE Advanced level
• A rigid insulated vessel is divided by a thin conducting partition. One side holds 2.00 mol of He at 300 K, the other 3.00 mol of N2 (rigid diatomic) at 460 K. ... JEE Advanced level
• The molar heat capacity of an ideal gas is C_P,m = 25.0 + 0.0200 T J mol^-1K^-1 (T in K). With R = 8.314 J mol^-1K^-1, the change in internal energy when one mo... JEE Advanced level
• One mole of a monatomic ideal gas is taken along the reversible path PV^2 = constant from 300 K to 360 K (R = 8.314 J mol^-1K^-1). For a polytropic path PV^n = ... JEE Advanced level
• For one mole of an ideal gas, the difference C_P - C_V equals NEET level
• Taking R = 8.314 J mol^-1K^-1, the molar heat capacity at constant volume of a monatomic ideal gas is nearest to NEET level
• The ratio gamma = C_P/C_V for a rigid diatomic ideal gas (translation and rotation only) is NEET level
• Taking R = 8.314 J mol^-1K^-1, the heat needed to raise the temperature of 1 mol of a monatomic ideal gas by 10 K at constant volume is nearest to NEET level
• A mixture contains 2 mol of helium and 3 mol of hydrogen (rigid diatomic). Treating both as ideal, the ratio C_P/C_V of the mixture is nearest to JEE Main level
• A polyatomic ideal gas has gamma = C_P/C_V = 1.30. Taking R = 8.314 J mol^-1K^-1, find C_V in J mol^-1K^-1 (two decimals). JEE Main level
• Argon (molar mass 40 g mol^-1) behaves as a monatomic ideal gas. Taking R = 8.314 J mol^-1K^-1, its specific heat capacity at constant pressure is nearest to JEE Main level
• Two moles of an ideal diatomic gas are heated by 50 K, once at constant pressure and once at constant volume. Taking R = 8.314 J mol^-1K^-1, find the difference... JEE Main level
• A non-linear polyatomic ideal gas has three translational and three rotational degrees of freedom and no vibrational contribution. Its gamma = C_P/C_V is JEE Main level
• One mole of a monatomic ideal gas is heated from 300 K to 400 K in a rigid vessel. Taking R = 8.314 J mol^-1K^-1, the enthalpy change Delta H is nearest to JEE Main level
• Select all correct statements for ideal gases. JEE Main level
• A mixture of 1 mol helium and 2 mol nitrogen (rigid diatomic) is heated at constant pressure from 300 K to 500 K. Treating the gases as ideal with R = 8.314 J m... JEE Advanced level
• A mixture of helium (monatomic) and hydrogen (rigid diatomic), both ideal, has C_P/C_V = 1.52. Find the mole percent of helium in the mixture (nearest integer). JEE Advanced level
• A sample of 0.50 mol of an ideal gas absorbs 727.5 J of heat at constant pressure and its temperature rises by 50.0 K. Taking R = 8.314 J mol^-1K^-1, find gamma... JEE Advanced level
• For one mole of a monatomic ideal gas, the molar heat capacity C along a reversible path PV^n = constant is C = C_V + R/(1-n). Select all correct statements. JEE Advanced level
• For an ideal gas the molar heat capacity at constant volume varies as C_V = 20.0 + 0.010 T J mol^-1K^-1. Taking R = 8.314 J mol^-1K^-1, the enthalpy change of o... JEE Advanced level
• One mole of helium at 300 K and two moles of nitrogen (rigid diatomic) at 450 K are mixed in a rigid, adiabatic container. Treating the gases as ideal, the fina... JEE Advanced level
• An ideal gas has C_P = 4.5R per mole, with R = 8.314 J mol^-1K^-1. Select all correct statements. JEE Advanced level