A heat engine has an efficiency of frac{1}{6} . When temeprature of sink is reduced by 62^{circ} {C}

English

Gujarati

Hindi

11.Thermodynamics

normal

A heat engine has an efficiency of $\frac{1}{6}$. When the temeprature of sink is reduced by $62^{\circ} {C}$, its efficiency get doubled. The temeprature of the source is $.....^{\circ} {C}$

A

$37$

B

$99$

C

$62$

D

$124$

Solution

Using, $\eta=1-\frac{ T _2}{ T _1}$

or $\frac{T_2}{T_1}=1-\eta$

According to first case

$\frac{ T _2}{ T _1}=1-\frac{1}{6}=\frac{5}{6} \ldots .$. (i)

According to second case

$\frac{ T _2-62}{ T _1}=1-2 \times \frac{1}{6}=\frac{2}{3} \ldots \ldots$. (ii)

$\frac{ T _2}{ T _1}-\frac{62}{ T _1}=\frac{2}{3}$

From equations $(i)$ and $(ii)$, we get

$\frac{5}{6}-\frac{62}{ T _1}=\frac{2}{3} \Rightarrow \frac{5}{6}-\frac{2}{3}=\frac{62}{ T _1}$

$\Rightarrow \frac{1}{6}=\frac{62}{ T _1}$

$T _1=372 K \text { or } T _1=372-372$

$T _1=99^{\circ} C$

Standard 11

Physics

Share

Similar Questions

$P-V$ diagram of $2\,g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?

normal

The isothermal Bulk modulus of an ideal gas at pressure $P$ is

normal

The efficiency of Carnot engine is $50\%$ and temperature of sink is $500\,K.$ If the temperature of source is kept constant and its efficiency is to be raised to $60\%$ then the required temperature of sink will be ……….. $\mathrm{K}$

normal

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$ , while box $B$ contains one mole of helium at temperature $(7/3)\, T_0$ . The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes), then the final temperature of gases $T_f$ , in terms of $T_0$ is

normal

A carnot engine working between $400\, K$ and $800 \,K$ has a work output of $1200\, J$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle …. $J$ ?

normal