Results 1 to 2 of 2

Math Help - Q = mcΔT problem

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    135

    Q = mcΔT problem

    When you take a bath, how many kg of hot water (49 C) must you mix with cold water (13 C) so that the temperature of the bath is 36 C? The total mass of the water (hot and cold) is 191 kg.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    When mixing hot water with cold, the resultant solution will reach its equilibrium temperature where the hot water loses heat and the cold water takes in heat. So:

    \begin{aligned} Q_{\text{cold}} & =  -Q_{\text{hot}} <br />
\\ (m c \Delta T)_{\text{cold}} & =  - (mc\Delta T)_{\text{hot}}<br />
\\ m_{\text{cold}} \cdot 4.184 \frac{J}{g ^{\circ}C} \cdot \left(36 ^{\circ}C - 13 ^{\circ} C\right) & = - \bigg( m_{\text{hot}} \cdot 4.184 \frac{J}{g ^{\circ}C} \cdot \left(36 ^{\circ} C - 49 ^{\circ} C\right) \bigg)<br />
\end{aligned}

    Now, we have two variables to deal with and we only want to solve for m_{\text{hot}}. Remember, what they gave you? The total mass of both hot and cold water is 191 kg, i.e. m_{\text{cold}} + m_{\text{hot}} = 191 which means: m_{\text{cold}} = 191 - m_{\text{hot}}

    Substitute that in and you should be able to solve for m_{\text{hot}}
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum