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Two moles of ideal helium gas are in a r...

Two moles of ideal helium gas are in a rubber balloon at `30^@C.` The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to `35^@C.` The amount of heat required in raising the temperature is nearly (take R
`=8.31 J//mol.K`)

A

`62 J`

B

`104 J`

C

`124 J`

D

`208 J`

Text Solution

Verified by Experts

The correct Answer is:
d
According to `I^(st)` law of thermodynamics,
`Delta Q = Delta U + Delta W = nC_(V) Delta T + nRDelta T`
` = n (3/2 R) Delta T + nRDelta T = n R Delta T (5/2)`
Here, `n = 2 , R = 8.31 ` J/mol K,
`Delta T = 35^(@) C - 30^(@) C = 5^(@) C`
`:. Delta Q = 2 xx 8.31 xx 5 (5/2) = 207 . 75 = 208 J`
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