Question

A 1.90-mol sample of hydrogen gas is heated at constant pressure from 306 K to 410 K. (a) Calculate the energy transferred to the gas by heat. 5.747 kJ Correct: Your answer is correct. (b) Calculate the increase in its internal energy. 4.105 kJ Correct: Your answer is correct. (c) Calculate the work done on the gas. -1.642 kJ Correct: Your answer is correct.

Answer 1

a. Q = 5.711 kJ

b. ΔE = 4.051 kJ

c. W = -1.660 kJ

Step-by-step explanation:

1a. The amount of energy transferred to a gas when heated at constant pressure is given as Q = nCpΔT

where n = number of moles of gas;

Cp = molar specific heat of the gas at constant pressure,

ΔT = temperature change

From the given data; n = 1.90 moles , Cp of hydrogen gas (from tables) = 28.9 J/mol/K, ΔT = 104 K

Substituting the given values:

Q = 1.90 * 28.9 * 104

Q = 5710.64 J

Q = 5.711 kJ

b. The change in internal energy of a confined gas that undergoes a temperature change due to any process is given by the formula: ΔE = nCvΔT

where n = number of moles of gas;

Cv = molar specific heat of the gas at constant volume,

ΔT = temperature change

From the given data; n = 1.90 moles , Cv of hydrogen gas (from tables) = 20.4 J/mol/K, ΔT = 104 K

substituting the values

ΔE = 1.90 * 20.5 * 104

ΔE = 4050.8 J

ΔE = 4.051 kJ

c. From the first law of thermodynamics, ΔE = Q + W

where W is work done on the system.

from our calculations, ΔE = 4.051 kJ, Q = 5.711 kJ

W = ΔE - Q

W = (4.051 - 5.711) kJ

W = -1.660 kJ