What is the change in internal energy of the gas?
A 100W electric heater (1W=1J/s) operates for 6.5 min to heat the gas in a cylinder. At the same time, the gas expands from 1L to 15L against a constant atmospheric pressure of 3.627 atm. What is the change in internal energy of the gas? Answer in units of kJ.
Show work please!
The amount of heat transferred to the gas is.
Q = P·Δt= 100W · (6.5·60s) = 39000 J
Work done on the gas is given by the integral:
W = – ∫V₁→V₂ p dV
for constant p this simplifies to:
W = – p·(V₂ – V₁)
Hence:
(since Pa·m³ = J convert pressure to Pa and Volume to m³)
W = – (3.627·101325Pa) · ( 0.015m³ – 0.001m³)
= -5145J
So the change of internal energy of the gas is
ΔU = Q + W = 39000J – 5145J = 33855J
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