- #1
SoggyBottoms
- 59
- 0
Homework Statement
An ideal gas of N particles is reversibly expanded from V1 to V2 = 4V1. The starting temperature T1 is known and [itex]E_1 = \frac{3}{2} N k_B T_1[/itex]. As of yet [itex]E_2[/itex] is unknown.
a) Express [itex]\Delta E = E_1 - E_2[/itex] in terms of the added heat Q and work done on the gas W.
b) Calculate the work done W if the expansion is isobaric.
c) Calculate Q, W and [itex]E_2[/itex] if the expansion is isothermal.
d) Calculate Q if the expansion is adiabatic.
e) If the expansion in question d) was irreversible instead of reversible, would the added heat be less, more or equal?
The Attempt at a Solution
a) The gas does positive work, so the work done on the gas is negative: [itex]\Delta E = Q - W[/itex]
b) For an isobaric expansion: [itex]W = p(V_2 - V_1) = 3V_1p[/itex]
c) [itex]dW = pdV[/itex], so [itex]W = \int_{V_1}^{V_2} \frac{N k_B T_1}{V} dV = N k_B T_1 \ln{\frac{4 V_1}{V_1}} = N k_B T_1 \ln{4}[/itex]
[itex]Q = W = N k_B T_1 \ln{4}[/itex]
[itex]dU = 0[/itex], so there is no change in energy: [itex]E_1 = E_2 = \frac{3}{2}N k_B T_1[/itex]
d) In an adiabatic expansion Q = 0.
e) If the expansion was irreversible, then heat was lost on friction or something else, so to make up for that, the added heat would have to be more than 0.
Can someone check these answers? I am doubting most of them.