Answer :
The amount of energy needed to increase the temperature of a substance by [tex]\Delta T[/tex] is given by:
[tex]Q=m C_s \Delta T[/tex]
where
m is the mass of the substance
Cs is the specific heat capacity of the substance
[tex]\Delta T[/tex] is the increase in temperature
In our problem, m=50.0 g, [tex]C_s = 4.18 J/g ^{\circ}C[/tex] (specific heat capacity of water) and [tex]\Delta T=15.0 ^{\circ}C[/tex], therefore the amount of energy needed is
[tex]Q=mC_s \Delta T=(50.0 g)(4.18 J/g^{\circ}C)(15.0^{\circ}C)=3135 J[/tex]
[tex]Q=m C_s \Delta T[/tex]
where
m is the mass of the substance
Cs is the specific heat capacity of the substance
[tex]\Delta T[/tex] is the increase in temperature
In our problem, m=50.0 g, [tex]C_s = 4.18 J/g ^{\circ}C[/tex] (specific heat capacity of water) and [tex]\Delta T=15.0 ^{\circ}C[/tex], therefore the amount of energy needed is
[tex]Q=mC_s \Delta T=(50.0 g)(4.18 J/g^{\circ}C)(15.0^{\circ}C)=3135 J[/tex]
3135 J of energy is needed to change the temperature of 50g of water by [tex]\rm 15^\circ C[/tex].
Given :
Mass of water is 50g
Change in temperature = [tex]\rm 15^\circ C[/tex]
Solution :
We know that energy needed to increase the temperature of a substance is,
[tex]\rm Q = mC_s \Delta T[/tex] ---- (1)
where,
m is the mass of the substance,
[tex]\rm C_s[/tex] is the specific heat capacity of the substance,
[tex]\rm C_s = 4.18 \; J/g ^\circ C[/tex] --- (specific heat of water)
and [tex]\rm \Delta T[/tex] is the change in temperature.
Now put the values of [tex]\rm m,\;\Delta T\; and \; C_s[/tex] in equation (1) we get,
[tex]\rm Q = 50\times 4.18 \times 15[/tex]
[tex]\rm Q = 3135\;J[/tex]
3135 J of energy is needed to change the temperature of 50g of water by [tex]\rm 15^\circ C[/tex].
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