Question

A gas in a cylinder expands from a volume of 0.110 m³ to 0.320 m³. heat flows into the gas just rapidly enough to keep the pressure constant at 1.65×10⁵ during the expansion. the total heat added is 1.15×10⁵ j. find the change in internal energy of the gas.

Answer 1

80000 Joule is the change in the internal energy of the gas.

In Thermodynamics, work done by the gas during expansion at constant pressure:

ΔW = -pdV

ΔW = -pd (V₂ -V₁)

ΔW = - 1.65×10⁵ pa (0.320m³ - 0.110m³)

     = - 0.35×10⁵ pa.m³

     = - 35000 (N/m³)(m³)

     = -35000 Nm

ΔW = -35000 Joule

Therefore, work done by the system = -35000 Joule

Change in the internal energy of the gas,

ΔV = ΔQ + ΔW

Given:

ΔQ = 1.15×10⁵ Joule

ΔW = -35000 Joule

ΔU = 1.15×10⁵ Joule - 35000 Joule

      = 80000 Joule.

Therefore, the change in the internal energy of the gas= 80000 Joule.

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