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Question
70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
Options
30 calories
50 calories
70 calories
90 calories
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Solution
50 calories
It is given that 70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. Also, specific heat at constant pressure,
`"C"_"P" = (triangle Q)/(ntriangleT)`
`=> "C"_"P" = 70/ (2 xx (35-30)`
`=> "C"_"P" =70/(2 xx 5)`
`=> "C"_"P" = 7 "calories" -" mol" ^-1K^-1`
For an ideal gas ,
CP - CV = R = 8.314 J - mol -1 K-1 ≃ 2 calories mol-1K-1
⇒ CV =CP -R
⇒ CV = (7-2) calories - mol-1 K-1
⇒ CV = 5 calories - mol-1 K-1
⇒ CV = `(triangle "Q")/(ntriangle"T")`
`=> 5 = (triangle "Q")/(2 xx (35-30)`
⇒ Δ Q = 5 × 2 × (35-30)
⇒ Δ Q = 5 × 2 × 5
⇒ Δ Q = 50 calories
Therefore, 50 calories need to be supplied to raise the temperature of 2 moles of gas from 30-35 oC at constant volume.
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