3.100 Work done in a cyclic process

Problem 3.100: Determine work done in a cyclic process with a $P-V$ diagram as shown here. Solution: Work done in acyclic process can be found by calculating the area enclosed in the $P-V$ diagram. Here the $P-V diagram is a rectangle. The volume varies from $V$ to...

3.99 Heat exchanged in two paths

Problem 3.99: A system goes from $A$ to $B$ by two different paths in the $P-V$ diagram as shown. Heat given to the system in path $1$ is $1000\: J$. The work done by the system along path $2$ is less than path $1$ by $100 \:J$. What is the heat exchanged by the...

3.98 Change in internal energy in adiabatic process

Problem 3.98: A thermally insulated vessel contains two moles of hydrogen gas. In a process its temperature changes from $200\:K$ to $300\:K$ adiabatically. Determine the change in internal energy of the gas. Solution: In adiabatic process, heat cannot be transferred...

3.97 Adiabatic work done

Problem 3.97: A thermally insulated vessel contains two moles of a mono-atomic gas. In a process its temperature changes from $200\:K$ to $300\:K$ adiabatically. Determine the work done in this process. Solution: Heat transferred $\triangle Q$ is related to change in...

3.96 Mean free path of molecules of a gas

Problem 3.96: A certain ideal gas has a temperature $300\:K$ and a pressure $5.0 \times 10^4 \:Pa$. The molecules have a mean free path of $4.0 \times 10^{−7}\: m$. Determine mean free path when the temperature is raised to $350\:K$ and the pressure is reduced to $1.0...

3.95 Cubical expansion of a solid

Problem 3.95: The coefficient of linear expansion of steel is $1.1 × 10^{-5}\:^oC^{-1}$. A steel ball has a volume of exactly $100 cm^3$ at $0^oC$. Find its volume at $100^oC$. Solution: Change in any volume, $(\triangle V)$ is related to original volume $(V)$ as...

3.94 Expansion of a metal

Problem 3.94: A rectangular plate of glass initially has the dimensions $0.200\: m$ by $0.300 \:m$. The coefficient of linear expansion for the glass is $9.00\times 10^{-6}\:K^{-1}$. What is the change in the plate’s area if its temperature is increased by $20.0 \:K$?...

3.93 Thermal expansion

Problem 3.93:3.93 Thermal expansion A circular iron disc has a circular hole of radius $10\:cm$ at its center. The temperature of the disc is changed from $100^oC$ to $200^oC$. Find the radius of the hole at the new temperature. Coefficient of linear expansion of iron...

3.92 Translational kinetic energy of a gas molecule

Problem 3.92: A  closed container encloses $3$ moles of hydrogen at a temperature of $300\:K$. Determine the translational kinetic energy of a molecule. $($ Diagram is only representational $)$ Solution: According to kinetic theory of gases, molecules possess kinetic...

3.91Rate of transfer of heat

Problem 3.91: Two metallic plates kept at temperatures of $T$ and $2T$ are connected by two metallic rods of same length $L$ but area of cross sections $A$ and $3A$ as shown in the given diagram. The thermal conductivities of the two rods are $3K$ and $K$...

3.90 Isobaric expansion

Problem 3.90: Air enters a hot-air furnace at $7^Oc$ and leaves at $77^Oc$. Throughout the process pressure does not change. It is seen that each entering cubic meter of air expands to $X$ cubic meter. Find the value of $X$. Solution: Clearly this is an isobaric...

3.89 Adiabatic expansion of a gas

Problem 3.89:3.89 Adiabatic expansion of a gas$1$ mol of oxygen $($assumed to be an ideal gas$)$ has temperature $310 K $and volume $12 L$. What would be the final temperature if the gas expands adiabatically to volume $19 L$? Oxygen (O2) is diatomic and here has...

3.88 Change in internal energy of air

Problem 3.88: A typical room contains about $3000$ moles of air. Find the change in the internal energy of this much air when it is cooled from $35\:^oC$ to $22\:^oC$ at a constant pressure of $1.00 \:atm$. Assume air as an ideal gas with molar specific heat capacity...

3.87 Heat emission and absorption

Problem 3.87: A blackened solid copper sphere of radius $2\:cm$ is placed in an evacuated enclosure whose walls are kept at $100\:^oC$. At what rate must energy be supplied to the sphere to keep its temperature constant at $127\:^oC$? Stefan constant $=\:5.67\times...

3.86 Change in entropy of a system

Problem 3.86: $250\:g$ of steam at $100\:^oC$ is condensed to water at the same temperature. Determine the change in entropy. Latent heat of vaporization of water is $22.6\times 10^5\:Jkg^{-1}$. Solution: Entropy $(S)$ is a quantitative measure of the disorder of a...

3.85 Rate of heat received

Problem 3.85: A room is lighted by four 100 W incandescent light bulbs. Assuming that $70$ % of the energy is converted to heat, how much heat does the room receive in $6$ hours ? Solution: Power of electric bulb is the rate at which electrical energy is converted...

3.84 Expansion at constant pressure

Problem 3.84: A gas is contained in a closed vessel with an initial volume of $1\:m^3$ at a pressure of $1 bar$ and temperature of $15^oC$. The gas is heated at constant pressure to raise its temperature from $15^oC$ to $250^oC$. Determine the work done during the...

3.83 Equilibrium temperature

Problem 3.83: A thermally insulated chamber encloses two identical copper blocks of mass $1.5\: kg$ each. Block $A$ is at temperature $ 60^o C$  and block $B$ at temperature $ 20^oC$. The blocks eventually come to the equilibrium with each other. Determine the...