A gas expands from 3 d m 3 to 5 d m 3 against a constant pressure of 3 atm. The work done during expansion is used to heat 10 mole of water at temperature 290 K. Calculate final temperature of water.

Question

A gas expands from 3 d m 3 to 5 d m 3 against a constant pressure of 3 atm. The work done during expansion is used to heat 10 mole of water at temperature 290 K. Calculate final temperature of water. Specific heat of water = 4.184 J/ g/K. [Given: 1 atm = 101.33 J]

TestHub · Accepted Answer

Work is done against constant P Δ V = 5 - 3 = 2 d m 3 = 2 l i t r e ; P = 3 a t m ∴ W = - P Δ V = - 3 × 2 l i t r e a t m = − 6 × 101.33 = − 608 J Now, this work is used up in heating water ∴ W = n × C × ΔT 608 = 10 × 4.184 × 18 Δ T ∴ Δ T = 0.81 ∴ F i n a l t e m p e r a t u r e = T 1 + Δ T = 290 + 0.81 = 290.81 K

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