Lesson test: Work, heat and the First Law

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Work, heat and the First Law

1.[2p]
With the convention that work done on the system is positive, what is the sign of $W$ when a gas expands?

Negative, because $d V$ is positive and $δ W = - p d V$

Correct

Positive, because the gas is doing work

The answer is: Negative, because $dV$ is positive and $\delta W = -p\,dV$

Negative, because heat must leave the gas

The answer is: Negative, because $dV$ is positive and $\delta W = -p\,dV$

Positive, because the volume increases

The answer is: Negative, because $dV$ is positive and $\delta W = -p\,dV$

2.[1p]
The derivation of $δ W = - p d V$ for a piston of area $A$ uses which two substitutions?

Force is $p A$ , and the swept volume is $A d x$

Correct

Force is $p / A$ , and the swept volume is $A d x$

The answer is: Force is $pA$, and the swept volume is $A\,dx$

Force is $p A$ , and the swept volume is $d x / A$

The answer is: Force is $pA$, and the swept volume is $A\,dx$

Force is $m g$ , and the displacement is $d V / A$

The answer is: Force is $pA$, and the swept volume is $A\,dx$

3.[2p]
Rumford's cannon-boring observation at Munich in 1798 was fatal to caloric theory because

friction produced heat without apparent limit, and a conserved substance cannot be created

Correct

the borings had a different specific heat from the parent metal

The answer is: friction produced heat without apparent limit, and a conserved substance cannot be created

the water boiled faster than caloric could have flowed into it

The answer is: friction produced heat without apparent limit, and a conserved substance cannot be created

heat was seen to flow from a cold body to a hot one

The answer is: friction produced heat without apparent limit, and a conserved substance cannot be created

4.[1p]
Joule's 1850 value for the mechanical equivalent of heat was within about one per cent of the modern value.

True

Correct

False

The answer is: True

5.[3p]
Why is heat defined as $Q = Δ U - W$ rather than assumed as a primitive quantity?

Because $U$ can be established first, from the path independence of adiabatic work, using only measurements of work

Correct

Because heat cannot be measured by any experiment

The answer is: Because $U$ can be established first, from the path independence of adiabatic work, using only measurements of work

Because $Q$ is an exact differential and $W$ is not

The answer is: Because $U$ can be established first, from the path independence of adiabatic work, using only measurements of work

Because the definition makes $Q$ independent of the path taken

The answer is: Because $U$ can be established first, from the path independence of adiabatic work, using only measurements of work

6.[2p]
Which of these statements about $\oint d U$ and $\oint δ Q$ are correct?

Select all that apply

$\oint d U = 0$ for every cycle

Correct

$\oint δ Q$ can be non-zero for a cycle

Correct

Over a cycle, $\oint δ Q = - \oint δ W$

Correct

$\oint δ W = 0$ for every cycle

The answer is: $\oint dU = 0$ for every cycle, $\oint \delta Q$ can be non-zero for a cycle, Over a cycle, $\oint \delta Q = -\oint \delta W$

7.[2p]
One mole of an ideal gas expands reversibly and isothermally at 300 K from 12.47 L to 24.94 L. How much work in joules is done ON the gas? Give the signed value.

CorrectNot quite: -1728.9

8.[3p]
One mole of an ideal monatomic gas is heated from 300 K to 600 K at a constant pressure of 200 kPa, its volume doubling from 12.471 L to 24.942 L. How much heat in joules enters the gas?

CorrectNot quite: 6235.5

9.[2p]
Match each kind of work to its generalised force.

Boundary displacement
Stirring a fluid
Stretching a wire
Extending a liquid film

tension
pressure
surface tension
torque

Show the answer

Boundary displacement: pressure Stirring a fluid: torque Stretching a wire: tension Extending a liquid film: surface tension

10.[2p]
A machine that absorbs heat from the ocean and converts all of it into work in a cycle is

allowed by the First Law but forbidden by the Second

Correct

forbidden by the First Law, since it creates energy

The answer is: allowed by the First Law but forbidden by the Second

perpetual motion of the first kind

The answer is: allowed by the First Law but forbidden by the Second

allowed, and has been built

The answer is: allowed by the First Law but forbidden by the Second

1.[2p] With the convention that work done on the system is positive, what is the sign of W when a gas expands?

2.[1p] The derivation of δW=-pdV for a piston of area A uses which two substitutions?

3.[2p] Rumford's cannon-boring observation at Munich in 1798 was fatal to caloric theory because

4.[1p] Joule's 1850 value for the mechanical equivalent of heat was within about one per cent of the modern value.

5.[3p] Why is heat defined as Q=ΔU-W rather than assumed as a primitive quantity?

6.[2p] Which of these statements about ∮dU and ∮δQ are correct?

7.[2p] One mole of an ideal gas expands reversibly and isothermally at 300 K from 12.47 L to 24.94 L. How much work in joules is done ON the gas? Give the signed value.

8.[3p] One mole of an ideal monatomic gas is heated from 300 K to 600 K at a constant pressure of 200 kPa, its volume doubling from 12.471 L to 24.942 L. How much heat in joules enters the gas?

9.[2p] Match each kind of work to its generalised force.

10.[2p] A machine that absorbs heat from the ocean and converts all of it into work in a cycle is

1.[2p]
With the convention that work done on the system is positive, what is the sign of $W$ when a gas expands?

2.[1p]
The derivation of $δ W = - p d V$ for a piston of area $A$ uses which two substitutions?

3.[2p]
Rumford's cannon-boring observation at Munich in 1798 was fatal to caloric theory because

4.[1p]
Joule's 1850 value for the mechanical equivalent of heat was within about one per cent of the modern value.

5.[3p]
Why is heat defined as $Q = Δ U - W$ rather than assumed as a primitive quantity?

6.[2p]
Which of these statements about $\oint d U$ and $\oint δ Q$ are correct?

7.[2p]
One mole of an ideal gas expands reversibly and isothermally at 300 K from 12.47 L to 24.94 L. How much work in joules is done ON the gas? Give the signed value.

8.[3p]
One mole of an ideal monatomic gas is heated from 300 K to 600 K at a constant pressure of 200 kPa, its volume doubling from 12.471 L to 24.942 L. How much heat in joules enters the gas?

9.[2p]
Match each kind of work to its generalised force.

10.[2p]
A machine that absorbs heat from the ocean and converts all of it into work in a cycle is