Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is 0.300 m and the length of the copper section is 0.800 m. Each segment has cross-sectional area 0.00500 m$^2$. The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice–water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings. (a) What is the temperature of the point where the brass and copper segments are joined? (b) What mass of ice is melted in 5.00 min by the heat conducted by the composite rod?
Temperature and Heat
well, heat flow from browse to the cooper. Uh, therefore, we have, um minus Q divided by two minus. Ah kun, divided by t is equal to Q divided pike T Well, this is for brass on. This is for Cooper on DDE. This can be returnees minus into kim. Multiply by a multiplying die delta T divided by our is equal to key. And this is for Russ. Multiply by a multiplied by delta t divided by, uh oh, for Cooper. Andi simplifying this a simplifying and plugging the values we have, uh, minus into key for brass into t two minus 100 divided by lend off. Brass is equal to gay for copper into t to minus zero. Divided by lend off copper. See you. Well, no. Let's, uh fuck the values minus okay. Be care for brass is 109 into Tito minus 100 divided by lent off bras is, uh, 0.20 zero meters. It's a cold too. We'll care for copper gave for cooperate is created five into t to minus zero divided by zero point it maker. So lent of copper reality 0.8 meters and therefore we have for 36 into 100 minus t two is we call to 300 85 times Tito and Soling 42. We have tea, too. Physical toe. 53 0.1 Decree Sandy grade. All right, now, let's so part B to calculate the Maas If eyes, which is melted after five minutes, we would calculate the heat off the phase transition on Kim is equal to moss off ice multiply by late and Tito fusion. And this is a call to minus two key. Multiply by a multiply by t time Small Ty's time multiply with Delta Captain T Was his changing temperature divided by lend l Okay, so from this we have Marce off ice is equal to he multiplied by a multiplied by t multiply by delta t divided by l multiply by lightened heat off fusion. All right, let's split the values now. Months off ice is equal to 109 Well, nine one Or mine is the value of key. Multiply by A, which is 0.5 meter square multiply by five minutes, which is equal to 300 seconds multiplied by change in temperature. His 100 minus 53 100 minus 53 divided by Lenk, lengthy 0.200 multiplied by Light and Tito Fusion. And it's equal to 334 Multiply that I turned to the power pre Jules her kilogram. So solving this mar selfies is a cool too little point 115 kilogram. End of the problem. Thank you for watching.