(Solved): The temperatures at the ends of a bar are \( T_{w}=88^{\circ} \mathrm{C} \) at the warmer end and \ ...

The temperatures at the ends of a bar are \( T_{w}=88^{\circ} \mathrm{C} \) at the warmer end and \( T_{c}=23^{\circ} \mathrm{C} \) at the cooler end. The bar has a length of \( L=0.73 \mathrm{~m} \). What is the temperature at a point that is \( D=0.35 \) \( \mathrm{m} \) from the cooler end of the bar? Please round your answer to one decimal place. Equation: The heat conducted during time t through the entire length \( \mathrm{L} \) of the bar and crosssectional area \( A \) is: \( Q=\frac{k A\left(T_{v}-T_{c}\right) t}{L} \quad k \) is the thermal conductivity, \( T_{w} \) is the temperature at the warmer end of the bar and \( T_{c} \) is the temperature at the cooler end of the bar. Similarly, the heat conducted during time \( t \) through the length \( D \) between the point in question and the cooler end of the bar and cross-sectional area \( A \) is: \( Q=\frac{k A\left(T-T_{0}\right) t}{D} \quad k \) is the thermal conductivity. \( T \) is the temperature at the point in question and \( T_{c} \) is temperature at the cooler end of the bar. Note: \( Q f, A \) and \( k \) are the same for the two equations. Solve for \( T \).