To determine the correct signs of heat ([tex]\( Q \)[/tex]) and work ([tex]\( W \)[/tex]) when the gas in a balloon is heated and the balloon expands, we need to consider the principles of thermodynamics.
### Step-by-Step Solution:
1. Heating the gas (Absorbing Heat):
- When the gas inside the balloon is heated, it absorbs heat from its surroundings.
- According to the convention in thermodynamics, when heat is absorbed by the system (the gas in this case), [tex]\( Q \)[/tex] is positive ([tex]\( +Q \)[/tex]).
2. Balloon Expansion (Doing Work):
- As the gas absorbs heat, it gains energy, causing it to expand and push against the walls of the balloon.
- This expansion means that the gas is doing work on its surroundings (the balloon and the external air).
- According to the convention in thermodynamics, when the system (the gas) does work on its surroundings, [tex]\( W \)[/tex] is considered negative ([tex]\( -W \)[/tex]).
Combining these two points, when the gas in the balloon is heated:
- Heat ([tex]\( Q \)[/tex]) is absorbed and is positive.
- Work ([tex]\( W \)[/tex]) is done by the gas during expansion and is negative.
Thus, the correct signs for heat and work during this change are:
[tex]\[ +Q, -W \][/tex]
### Answer:
[tex]\[ \boxed{D. +Q, -W} \][/tex]
