Exam 15: The Laws of Thermodynamics

A gas expands from an initial volume of $0.040 \mathrm {~m} ^ { 3 }$ to a final volume of $0.085 \mathrm {~m} ^ { 3 }$ while its pressure increases linearly with the volume (so that the process follows a straight-line path in a $p V$ diagram) from $110 \mathrm { kPa }$ to $225 \mathrm { kPa }$ . How much work is done by the gas during this expansion?

The figure shows a $p V$ diagram for $0.0077$ mol of ideal gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . What is the volume $V _ { 3 }$ ? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$ $p$ (atm)

A gas follows the $p V$ trajectory shown in Figure 16.2. How much work is done per cycle by the gas if The gas in a heat engine follows the cycle shown in the $p V$ diagram. How much work does this engine do each cycle if $p _ { 0 } = 5.4$ atm?

The figure shows a $p V$ diagram for a cycle of a heat engine for which $Q \mathrm { H } = 59 \mathrm {~J}$ . What is the thermal efficiency of the engine?

An irreversible engine operating between the temperatures of $550 \mathrm {~K}$ and $300 \mathrm {~K}$ extracts $1.20 \mathrm {~kJ}$ of heat from the hot reservoir and produces $0.450 \mathrm {~kJ}$ of work. How much entropy is created in the process?

A 10-L flask and a 1-L flask each contain two moles of ideal diatomic gas (but not the same gas) at $25 ^ { \circ } \mathrm { C }$ . Which of the following statements about these gases must be true? (There could be more than one correct choice.)

A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the $p V$ diagram in the figure. If the process is carried out in a counter-clockwise sense around the enclosed area, as shown on the figure, then the magnitude of the enclosed area represents

A refrigerator has a performance coefficient (COP) of $1.15$ , and it extracts $7.95 \mathrm {~J}$ of heat from the cold reservoir during each cycle. (a) How much work is done on the gas in each cycle? (b) How much heat is exhausted into the hot reservoir in each cycle?

A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle. (a) How much work does it perform in each cycle? (b) How much heat does it exhaust in each cycle?

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $11.0 \%$ . What is the temperature of the warm reservoir?

What is the entropy change of $450 \mathrm {~g}$ of water when it changes from (a) liquid to steam at its usual boiling point and (b) ice to liquid at its usual melting point? For water, $L _ { F } = 0.334$ $\mathrm { MJ } / \mathrm { kg } , L \mathrm {~V} = 2.26 \mathrm { MJ } / \mathrm { kg }$ .

The figure shows a $p V$ diagram for $0.0061$ mol of ideal gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . What is the pressure $p _ { 2 } ? ( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$ $p$ (atm)

For a certain ideal Carnot engine, the hot reservoir is $35 \mathrm { C } ^ { \circ }$ higher than the cold reservoir. If this engine is to have an efficiency of $20 \%$ , what must be the temperature of the hot reservoir?

An ideal gas undergoes the process $a \rightarrow b \rightarrow c \rightarrow a$ shown in the $p V$ diagram. The heat gained by the gas in process $a \rightarrow b$ is $546 \mathrm {~J}$ , while in process $b \rightarrow c$ the gas loses $62.0 \mathrm {~J}$ of heat. In process $a \rightarrow b$ the gas performs $310 \mathrm {~J}$ of work, while in process $c \rightarrow a 223 \mathrm {~J}$ of work is done on the gas. How much heat is gained by the gas in process $c \rightarrow a$ ?

Two ideal Carnot heat engines have the same efficiency. One operates between $5.0 \times 10 ^ { 2 } \mathrm {~K}$ and $3.0$ $\times 10 ^ { 2 } \mathrm {~K}$ , and the other between $4.0 \times 10 ^ { 2 } \mathrm {~K}$ and some lower temperature. What is the lower temperature?

A compression at a constant pressure of $200 \mathrm { kPa }$ is performed on $8.00$ moles of an ideal monatomic gas. The compression reduces the volume of the gas from $0.200 \mathrm {~m} ^ { 3 }$ to $0.120 \mathrm {~m} ^ { 3 }$ . How much work was done by the gas during this process?

The figure shows a $p V$ diagram for a gas going through a cycle from $A$ to $B$ to $C$ and back to A. From point $A$ to point $B$ , the gas absorbs $50 \mathrm {~J}$ of heat and finds its internal (thermal) energy has increased by $20 \mathrm {~J}$ . Going from B to $C$ , the internal (thermal) energy decreases by $5.0 \mathrm {~J}$ . (a) How much work was done by the gas from $A$ to $B$ ? (b) How much heat was absorbed by the gas from $B$ to $C$ ? (c) How much work was done by the gas going from $B$ to $C$ ?

A certain automobile engine takes in 4.00 kJ of heat and performs 1.10 kJ of mechanical work in each cycle. (a) Calculate the engine's efficiency. (b) How much heat is "wasted" in each cycle?

A Carnot cycle consists of

A Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at $67 \%$ efficiency, what is the ratio of the absolute temperatures of the reservoirs, $T _ { d } T _ { h }$ ?