Question

an ideal gas has C_v=(7/2)R. A 2.00 mole sample of gas starts at P=1*10^5 Pa and T=300K. determine the total P, V&T for each of the following cases, as well as ΔE_int, W and Q

a) gas is heated at constant P to 400K

b) gas is heated at constant V to 400K

c) isothermal conpression to P=1.2*10^5 Pa

d) adiabatic to compression P= 1.2*10^5

Answer 1

Initial Stage:
Pi = 1 x 10^5 Pa ; T = 300 K
PV = nRT
1 x 10^5 * V = 2*8.314*300
V = 0.0499 m^3 = 49.9 litres
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Stage a) P = 1 x 10^5 Pa ; T = 400 K
as P remains constant . isobaric process occurs here,
PV = nRT
1 x 10^5 *V = 2 *8.314*400
V = 0.0665 m^3 = 66.5 litres
W = nR(del T) = 2*8.314*100 = 1662.8 J
internal energy change, del U= n*C_v * (del T) = 700
Q = W + del U = 1662.8 +700 = 2362.8 J
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Stage b) V = 0.0499 m^3 = 49.9 litres ; T = 400 K
as V remains constant . isochoric process occurs here,
PV = nRT
P *0.0499 = 2 *8.314*400
P =1.33 x 10^5 Pa
W = 0 as change in volume = 0
internal energy change, del U= (3/2)*n*R*(del T) = 2494.2 J
Q = W + del U = 2494.2 J
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Stage c) P=1.2*10^5 Pa ; T = 300 K
as T remains constant . isothermal process occurs here,
PV = nRT
1.2*10^5 *V = 2 *8.314*300
V = 0.04157 m^3 = 41.57 litres
W = -nRT ln(V_f/V_i) = 2*8.314*300 ln (0.04157/0.0499) = -911.1 J
internal energy change, del U= 0
Q = W = -911.1 J