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An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0 × 105 Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas, (b) the number of moles in the gas if the initial temperature is 300 K, (c) the molar heat capacity Cp at constant pressure and (d) the molar heat capacity Cv at constant volume. 8. An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process.

An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0 × 105 Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas, (b) the number of moles in the gas if the initial temperature is 300 K, (c) the molar heat capacity Cp at constant pressure and (d) the molar heat capacity Cv at constant volume.
8. An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process.

Grade:10

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. V base 1 = 100 cm^3, V base 2 = 200 cm^3 P = 2 × 10^5 Pa, ∆Q = 50J (a) ∆Q = du + dw ⇒ 50 = du + 20× 10^5(200 – 100 × 10^–6) ⇒ 50 = du + 20 ⇒ du = 30 J (b) 30 = n × 3/2 * 8.3 * 300 [U = 3/2 nRT for monoatomic] ⇒ n = 2/3*83 = 2/249 = 0.008 (c) du = nC base vdT ⇒ C base v = dndTU/ = 30/0.008 * 300 = 12.5 C base p C base v + R = 12.5 + 8.3 = 20.3 (d) C base v = 12.5 (Proved above)

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