70 calories of heat required to raise the temperature of 2 moles of an ideal gas at constant pressure from `30^@Cto 35^@C.` The amount of heat required (in calories) to raise the temperature of the same gas through the same range `(30^@C to 35^@C)` at constant volume is:

Options

A. `50 cals`
B. `70 cals`
C. `60 cals`
D. `65 cals`

Answer

A

Explanation

From `DeltaQ = mC_(p)(DeltaT)`
`70 = 2 xx C_(p) xx (35 - 30)`,
`:. C_(p) = 70//10 = 7 cals//"mole"//.^(@)C`
`C_(v) = C_(p) - R = 7 - 2 = 5 cals//"mole"//.^(@)C`
`DeltaQ' = mC_(v)(DeltaT) = 2 xx 5 xx 5 = 50` cals