To answer the questions based on the information provided:
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Initial Temperature of the Container: The initial temperature is not specified in your prompt. However, to use gas laws, let’s assume it is the typical room temperature, which could be approximately 300K.
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Heat Addition Effect on Volume: When heat is added to the container, the temperature of the gas particles increases, which typically results in an increase in volume if pressure is held constant. Therefore, the volume increases with the addition of heat.
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Volume When Temperature is Lowered: If the temperature is lowered to half its initial temperature (from the assumed 300K to 150K), and assuming ideal gas behavior (Boyle's Law), the volume would also decrease to half its initial volume. Therefore:
- The new volume would be \(10 , \text{nm} / 2 = 5 , \text{nm}\).
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Volume When Temperature is Increased: If the temperature is increased to 5 times the initial temperature, the new temperature would be \(5 \times 300K = 1500K\). Again using the Ideal Gas Law logic, if the temperature increases, the volume will also increase proportionally:
- The new volume would be \(5 \times 10 , \text{nm} = 50 , \text{nm}\).
Summarizing:
- Initial temperature of the container: 300K (assumed)
- When temperature is half (150K), the new volume is: 5 nm
- If temperature is increased to 5x the initial temperature, the volume would be: 50 nm
Please ensure to insert the exact initial temperature if it was provided differently in your source material for accurate calculations.