# An object with a mass of #20 g# is dropped into #120 mL# of water at #0^@C#. If the object cools by #60 ^@C# and the water warms by #3 ^@C#, what is the specific heat of the material that the object is made of?

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Specific heat of the material = (\frac{{m \times c \times \Delta T_{\text{object}}}}{{m_{\text{water}} \times c_{\text{water}} \times \Delta T_{\text{water}}}}) Where: (m) = mass of the object (in grams) (c) = specific heat capacity of the material (in J/g°C) (\Delta T_{\text{object}}) = change in temperature of the object (in °C) (m_{\text{water}}) = mass of water (in grams) (c_{\text{water}}) = specific heat capacity of water (in J/g°C) (\Delta T_{\text{water}}) = change in temperature of water (in °C)

Given: (m = 20 \text{ g}) (\Delta T_{\text{object}} = -60 \text{ °C}) (negative because it cools) (m_{\text{water}} = 120 \text{ g}) (\Delta T_{\text{water}} = 3 \text{ °C}) (c_{\text{water}} = 4.18 \text{ J/g°C}) (specific heat capacity of water)

(c = \frac{{m \times c \times \Delta T_{\text{object}}}}{{m_{\text{water}} \times c_{\text{water}} \times \Delta T_{\text{water}}}}) (c = \frac{{20 \times c \times (-60)}}{{120 \times 4.18 \times 3}}) (c = \frac{{-1200 \times c}}{{1500.6}}) (c = \frac{{-1200}}{{1500.6 \times c}}) (c = \frac{{-1200}}{{1500.6}}) (c ≈ -0.799 \text{ J/g°C})

Therefore, the specific heat of the material that the object is made of is approximately (0.799 \text{ J/g°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.

- Some very hot rocks have a temperature of #150 ^o C# and a specific heat of #140 J/(Kg*K)#. The rocks are bathed in #14 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 #4 kg#, temperature of #261 ^oC#, and a specific heat of #8 (KJ)/(kg*K)# is dropped into a container with #39 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 #250 ^o C# and a specific heat of #160 J/(Kg*K)#. The rocks are bathed in #90 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 #18 g# is dropped into #240 mL# of water at #0^@C#. If the object cools by #120 ^@C# and the water warms by #6 ^@C#, what is the specific heat of the material that the object is made of?
- Gold has a specific heat of 0.129 J/g °C. How many joules of heat energy are required to raise the temperature of 16 grams of gold from 23 °C to 94 °C?

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