Given below are two statement
Statement $-I$ : What $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( P _{1}, V _{1}, T _{1}\right)$ to state $\left( P _{2}, V _{2}, T _{2}\right)$, the work done is $W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }}$ and $R =$ universal gas constant,
Statement $-II$ : In the above case. when work is done on the gas. the temperature of the gas would rise.
Choose the correct answer from the options given below
JEE MAIN 2022, Medium
Download our app for free and get started
$W _{\text {adiabatic }}=\frac{ NR \left( T _{f}- T _{ i }\right)}{1-\gamma} \rightarrow$ statment $1$
$Q=W+\Delta U$
$0= W +\Delta U$
$\Delta U =- W$
If work is done on the gas, i.e. work is negative
$\therefore \Delta U$ is positive.
$\therefore$ Temperature will increase.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^oC$View Solution
- 2A Carnot engine with efficiency $50\,\%$ takes heat from a source at $600\,K$. In order to increase the efficiency to $70\,\%$, keeping the temperature of sink same, the new temperature of the source will be $.........\,K$View Solution
- 3A solid body of constant heat capacity $1\ J/^o C$ is being heated by keeping it in contact with reservoirs in two ways :View Solution
$(i)$ Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies same amount of heat.
$(ii)$ Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies same amount of heat.
In both the cases body is brought from initial temperature $100^o C$ to final temperature $200^o C$. Entropy change of the body in the two cases respectively is :
- 4Efficiency of Carnot engine is $100\%$ ifView Solution
- 5Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600\,K$ and rejects heat to a reservoir at temperature $T$. Engine $B$ receives; heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are represented by ${\eta _A}$ and ${\eta _B}$ respectively, then what is the value of $\frac{{{\eta _A}}}{{{\eta _B}}}$View Solution
- 6An ideal gas at a pressures of $1$ atmosphere and temperature of ${27^o}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure, then the final temperature is ..... $^oC$ ($\gamma = 3/2$)View Solution
- 7The $P-V$ diagram of a certain process (carnot cycle) is as shown. The process is also represent asView Solution
- 8View SolutionThe temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
- 9If the amount of heat given to a system be $35$ joules and the amount of work done by the system be $ - 15$ joules, then the change in the internal energy of the system is .... $joules$View Solution
- 10A carnot engine with its cold body at $17\,^oC$ has $50\%$ effficiency. If the temperature of its hot body is now increased by $145\,^oC$, the efficiency becomes...... $\%$View Solution