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JEE Advanced levelSingle correct optionDifficulty 3 of 3td069

Five moles of an ideal gas absorb $6.00 kJ$ of heat at constant pressure, and the temperature rises by $20.0 K$ . Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , the change in internal energy of the gas is

A $6.83 kJ$
B $6.00 kJ$
C $5.17 kJ$
D $0.83 kJ$

Answer: C

At constant

P

,

q_{p} = n C_{p} Δ T

gives

C_{p} = 6000/ (5 \times 20) = 60.0 J mo l^{- 1} K^{- 1}

, so

C_{v} = C_{p} - R = 51.69

. Then

Δ U = n C_{v} Δ T = 5 \times 51.69 \times 20 = 5.17 kJ

(equivalently

q_{p} - n R Δ T = 6000 - 831.4 J

).

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