# A 25 g piece of an unknown metal alloy at 150°C is dropped into an insulated container with 200 g of ice. How do you calculate the specific heat capacity of the metal, given that 9.0 g of ice melted?

Moreover, we'll need the enthalpy of fusion for water,

Let's figure out how much heat was used to melt that ice,

Moreover, let's assume that the metal only released that heat and equilibrated with the ice,

This is fairly reasonable, most metals' specific heats are between 0 and 1. I'm open to feedback if I made a mistake!

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The specific heat capacity of the metal can be calculated using the formula:

( q_{\text{metal}} = -q_{\text{ice}} )

where ( q_{\text{metal}} ) is the heat gained by the metal, and ( q_{\text{ice}} ) is the heat lost by the ice.

The heat gained by the metal (( q_{\text{metal}} )) can be calculated using the formula:

( q_{\text{metal}} = mc\Delta T )

where:

- ( m ) is the mass of the metal (in grams)
- ( c ) is the specific heat capacity of the metal (in J/g°C)
- ( \Delta T ) is the change in temperature of the metal (final temperature - initial temperature)

The heat lost by the ice (( q_{\text{ice}} )) can be calculated using the formula for heat of fusion:

( q_{\text{ice}} = m_{\text{ice}} \times \Delta H_{\text{fusion}} )

where:

- ( m_{\text{ice}} ) is the mass of the ice that melted (in grams)
- ( \Delta H_{\text{fusion}} ) is the heat of fusion of ice (in J/g)

Once you have both ( q_{\text{metal}} ) and ( q_{\text{ice}} ), set them equal to each other and solve for the specific heat capacity of the metal (( c )).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- Does the type of liquid affect how fast an ice cube melts?

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