An ideal gas undergoes isothermal compression from an initial volume of 5.39 m3 to a final volume of 2.84 m3. there is 9.75 mol of the gas, and its temperature is 27.2°c. (a) how much work is done by the gas? (b) how much energy is transferred as heat between the gas and its environment?

a) Work done by gas = -15.584 KJ

b) Energy transferred = 15.584 KJ

Explanation:

Given:

Initial volume of the gas, V₁ = 5.39 m³

Final volume, V₂ = 2.84 m³

Temperature, T = 27.2°C = 273+27.2 = 300.2K

Number of moles, n = 9.75 mol

a) Work done for the given isothermal process is

where, R is the ideal gas constant = 8.31 J/mol.K

substituting the values we get,

or

b) From the first law of thermodynamics

change in internal energy = Heat added - Work done

or,

Now for the isothermal process, ΔU = 0

thus,

or

double the distance = divide strength by 4

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