Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

A diatomic gas of volume $2{ \mathrm{m}}^3$ at pressure $2\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$ is compressed adiabatically to a volume $0.5{ \mathrm{m}}^3.$ The work done in this process is,
[Use $4^{1.4}=6.96$]

$500 \mathrm{g}$ of water is heated from $30°\mathrm{C}$ to $90°\mathrm{C}.$ What is the change in its internal energy? (Specific heat of water is $4184 \mathrm{J}{ \mathrm{kg}}^{-1}{ \mathrm{K}}^{-1}$)

A tyre pumped to a pressure of $2$ atmosphere, suddenly bursts. If the temperature of air before expansion is $T$ then the air temperature after the tyre busts is
(Assume the expansion is adiabatic and adiabatic constant $\left.\gamma =\frac{3}{2}\right)$

An ideal gas undergoes an adiabatic process. If the pressure of the gas is reduced by $0.1\%$ then the volume is changed by (Given $r=\frac{C_p}{C_v}=\frac{5}{3}$)

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27°\mathrm{C}.$ The final temperature in Kelvins is
(use $\frac{C_P}{C_V}=\frac{5}{3}$)

Consider a two stage Carnot engine. In the first stage heat $Q_1$ is absorbed at temperature $T$ and heat $Q_2$ is expelled at temperature $\alpha T$ (where $\alpha <1$). In the second stage heat $Q_2$ is absorbed at temperature $\alpha T$ and heat $Q_3$ is expelled at temperature $\beta T(\beta <\alpha ).$ The efficiency of the Carnot engine will be

The carnot heat engine have an efficiency of $50\%.$ The temperature of sink is maintained at $500 \mathrm{K}.$ To increase the efficiency upto $80\%,$ the increment in the source temperature is

The following figure shows a Carnot engine that works between temperatures $T_1=400 \mathrm{K}$ and $T_2=200 \mathrm{K}$ and drives a Carnot refrigeration that works between temperatures $T_3=350 \mathrm{K}$ and $T_4=250 \mathrm{K}.$ The quantity $\frac{Q_3}{Q_1}$ will be