# An object with a mass of #120 g# is dropped into #500 mL# of water at #0^@C#. If the object cools by #30 ^@C# and the water warms by #16 ^@C#, what is the specific heat of the material that the object is made of?

The specific heat is

The heat is transferred from the hot object to the cold water.

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Use the formula ( Q = mc\Delta T ) where ( Q ) is the heat transferred, ( m ) is the mass, ( c ) is the specific heat, and ( \Delta T ) is the change in temperature. Rearrange the formula to solve for ( c ). The specific heat of the material is ( 0.63 , \text{J/g}^\circ\text{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.

- An object with a mass of #18 g# is dropped into #360 mL# of water at #0^@C#. If the object cools by #150 ^@C# and the water warms by #12 ^@C#, what is the specific heat of the material that the object is made of?
- An object with a mass of #6 kg#, temperature of #200 ^oC#, and a specific heat of #4 J/(kg*K)# is dropped into a container with #27 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?
- An object with a mass of #5 kg#, temperature of #123 ^oC#, and a specific heat of #14 J/(kg*K)# is dropped into a container with #32 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?
- Some very hot rocks have a temperature of #360 ^o C# and a specific heat of #180 J/(Kg*K)#. The rocks are bathed in #9 L# of boiling water. If the heat of the rocks completely vaporizes the water, what is the minimum combined mass of the rocks?
- An object with a mass of #3 kg#, temperature of #341 ^oC#, and a specific heat of #12 (KJ)/(kg*K)# is dropped into a container with #42 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?

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