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1.

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. The piston of A is free to move, while that B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30K, then the rise in temperature of the gas in B isA. `30 K`B. `18 K`C. `50 K`D. `42 K`

Answer» For cylinder `A : dQ=nC_(p)dT`
For cylinder `B : dQ=nC_(v)dT`
`rArr nC_(p)dT=nC_(v)dT`
`:. dT=(C_(p)xx30)/(C_(v))=30xx1.4=42K`
Discussion
2.

It takes `10 minutes` to cool a liquid from `61^(@)C` to `59^(@)C`. If room temperature is `30^(@)C` then find the time taken in cooling from `51^(@)C` to `49^(@)C`.A. `4` minuteB. `6` minuteC. `5` minuteD. `8` minute

Answer» Rate of cooling `alpha` difference in temperature
`(dT)/(dt) prop Delta theta rArr (dT)/(dt)=KDelta theta`
`dT=KDelta theta.dt`
In first case :
`dT=61-59=2`
`Deltatheta=60^(@)-30^(@)=30^(@)`
`dt=4"minute"`
`:. K=(dT)/(Deltatheta dt)=(2)/(30xx4)=(1)/(60)`
For second case :
`dT=2`
`Deltatheta=50-30=20`
`:. dt=(dT)/(KDeltatheta)=(2)/(.^(1)//_(60)xx 20)=6min`
Discussion
3.

Using the following data, find the change in temperature at which wood will just sink in benzene. Density of benzene at `0^(@)C=9xx10^(2)kgm^(-3)`, Density of wood at `0^(@)C=8.8xx10^(2)kgm^(-3)`, Cubical expansivity of benzene `=1.2xx10^(-3)K^(-1)` Cubical expansivity of wood `=1.5xx10^(-4)K^(-1)`

Answer» Let the subscript `1` and `2` denotes benzene and wood, respectively.
`:. (rho_(1))/(1+gamma_(1)DeltaT)=(rho_(2))/(1+gamma_(2)DeltaT)`
or `rho_(1)+rho_(1)gamma_(2)DeltaT=rho_(2)+rho_(2)gamma_(1)DeltaT`
or `DeltaT=(rho_(1)-rho_(2))/(rho_(2)gamma_(1)-rho_(1)gamma_(2))`
Here, `rho_(1)=900kgm^(3)`, `rho_(2)=880kg//m^(3)` , `gamma_(1)=1.2xx10^(-3)K^(-1)` ,
`gamma_(2)=1.5xx10^(-4)K^(-1)`
`:. DeltaT=21.7^(@)C`
Discussion