Question

a hot metal bar is put into a cup of cool water. what are the signs of $q$?
$q_{\text{water}}$ is
$q_{\text{bar}}$ is
water is turning a water wheel in a factory. what are the signs of $w$?
$w_{\text{water}}$ is
$w_{\text{factory}}$ is
in a steam engine, a flame heats up the steam causing it to expand. the piston is connected to a turbine that powers the factory. determine the signs for $q$ and $w$ for the steam in the cylinder.
$q_{\text{steam}}$ is
$w_{\text{steam}}$ is

Explanation:

Step1: Determine the sign of \( q \) for water and metal bar

• When a hot metal bar is put into cool water, heat flows from the metal bar to the water.
• By convention, \( q>0 \) if the system absorbs heat and \( q < 0 \) if the system releases heat.
• For water (\( q_{\text{water}} \)): Water absorbs heat, so \( q_{\text{water}}>0 \).
• For the metal bar (\( q_{\text{bar}} \)): The bar releases heat, so \( q_{\text{bar}}<0 \).

Step2: Determine the sign of \( w \) for water and factory

• When water turns a water - wheel in a factory, the water does work on the factory.
• By convention, \( w>0 \) if work is done on the system and \( w < 0 \) if work is done by the system.
• For water (\( w_{\text{water}} \)): Water does work (work is done by the water), so \( w_{\text{water}}<0 \).
• For the factory (\( w_{\text{factory}} \)): Work is done on the factory (by the water), so \( w_{\text{factory}}>0 \).

Step3: Determine the sign of \( q \) and \( w \) for steam in a steam engine

• In a steam engine, a flame heats the steam. So, the steam (\( q_{\text{steam}} \)) absorbs heat, \( q_{\text{steam}}>0 \).
• The steam expands and does work (on the piston which is connected to a turbine). So, work is done by the steam (\( w_{\text{steam}} \)), \( w_{\text{steam}}<0 \).

Answer:

• \( q_{\text{water}} \) is \(+\), \( q_{\text{bar}} \) is \(-\)
• \( w_{\text{water}} \) is \(-\), \( w_{\text{factory}} \) is \(+\)
• \( q_{\text{steam}} \) is \(+\), \( w_{\text{steam}} \) is \(-\)