University Physics AI No. 10 The First Law of Thermodynamics

Transcription

1 Unversty hyscs I No he Frst Law o hermodynamcs lass Number Name Ihoose the orrect nswer Whch o the ollowng processes must volate the rst law o thermodynamcs? (here may be more than one answer!) (,B,D ) () W >, <, and E nt (B) W >, <, and E nt > () W >, <, and E nt < (D) W <, >, and E nt < (E) W >, >, and E nt < pplyng the rst law o thermodynamcs E + W In whch o the paths between ntal state and nal state n Fg s the work done on the gas the greatest? ( D ) he work done by the gas s the area under the path, and the work done on the gas s the negatve o the work done by the gas onsder the ollowng processes that can be done on an deal gas: constant volume, ; constant pressure, ; and constant temperature, (a) For whch process does W? ( ) (b) For whch process does? ( D ) (c) For whch process does W+? ( D ) (d) For whch process does E nt? ( ) (e) For whch o these processes does E nt W? ( D ) () (B) () (D) Non o these pplyng the rst law o thermodynamcs B D Fg Whch o the ollowng processes s orbdden by the rst law o thermodynamcs? (here may be more than one correct answer!) () () n ce cube s placed n hot coee; the ce gets colder and the coee gets hotter (B) Sold wax s placed n hot metal pan; the wax melts and the metal pan cools () old s placed n a cold glass; the glass gets colder and the gets colder (D) student bulds an automoble engne that converts nto work the heat energy released when changed to ce (E) Dry ce can be made by allowng carbon doxde gas to expand n a bag Only ()volates the rst law o thermodynamcs

2 II Fllng the Blanks kg block o ce at - s placed n a punch bowl wth kg o (punch) at ssume no heat transer to the surroundngs and neglect the thermal eects o the punch bowl tsel Does all the ce melt? yes I not, the quantty whch s let s he nal temperature o the punch plus ce system s 8 K o warm the ce rom to takes a heat transer to the ce system mce ce ( + ) I all the ce melts, t need heat transer m L ce 667 Let the (punch) changes rom to, the heat transer s m 86 ( ) 88 So + < we can know all the ce wll melt s + + < So the system s nal temperature wll hgher than ssume that the nal temperature s o the punch plus ce system + + ( m + mce ) ( m + mce ) ( ) + + ( m + m ) ce ( + ) o 88( ) 8(K) typcal household heater has a capacty o about m o he s ntally at a temperature o and s warmed to 6 or the pleasure o long, hot showers he quantty o the heat transer whch s necessary to warm the s 9 7 J I the heatng element s rated at kw, the tme t take to warm the s h (a) he quantty o the heat transer whch s necessary to warm the s m ρ (b) t 86 (6 ) 9 7

3 t (s) (h) wo reservors, one at and the other at, are connected by means o two materals as ndcated n Fgure he relatve R-values o the materals are speced he temperature at the nterace between the two materals s 8 K ssume that the temperature s at the nterace between the two Hot reservor materals For d ), R d ( ) H ( R R R old reservor d d and ( ) ( ) So we have H R R RH + R R + R H + Fg (7 + ) + 7 8(K) gas s taken rom thermal equlbrum state to state on a - dagram va the semcrcular route ndcated n Fgure he work done by the gas n gong rom state to state s 6 J he work done by the gas t goes rom state back to state, retractng the semcrcular path s -6 J (a) he work s equal to the area under the semcrcular route 6 (atm) Fg (lters) W 6 ( ) (b) W W 6 π ( ) 6 B Gas wthn a chamber passes through the cycle shown n Fg he net heat added to the gas durng process J, and W J s -J Fg

4 U, U + W, U + W For the cycle, U U + U + U, hereore, + + W W J 6 Gas wthn a chamber undergoes the processes shown n the dagram o Fg he net heat added to the system durng one complete cycle s -8 J (Mpa) he work durng one complete cycle s equal to the area o the semcrcular route on the dagram: π W [( ) ] 8 pplyng the rst law o thermodynamcs: U + W (L) and U, so the net heat added to the system durng one complete cycle s W 8 J Fg III Gve the Solutons o the Followng roblems When a system s taken rom state to state along the path a n Fg6, t s ound that J and WJ long the path b, 6J (a) What s W along the path b? (b) I W-J or the curved return path, what s or ths path? (c) ake E nt, J What s E nt,? (d) I E nt,b J, nd or process b and prosess b (a) pplyng the rst law o thermodynamcs: U + W, a Fg6 b so U U U W, that s a Wa b Wb hus W + W b b a a (b) he same way as (a), we have a W a W So W + W 7 a a (c) pplyng the rst law o thermodynamcs: U + W, so

5 U E + nt Ent a Wa Ent a Wa + Ent (d) See the dagram, W W 6 J b b pplyng the rst law o thermodynamcs, the heat transer or process b s U + W Ent b Ent + Wb s +, so the heat transer or process b s b b b b b b hree () moles o an deal gas s taken along the excurson on a - dagram ndcated n Fgure 7 he rst part o the path s an sobarc process and the second part o the path s sothermal (a) What s the ntal absolute temperature o the gas? (b) alculate the work done by the gas along the sobarc segment o the path (c) What s the temperature o the gas along the sotherm? (d) Is the work done by the gas postve or negatve along the sothermal segment o the path? (e) Determne the nal volume o the gas so that the total work done by the gas s zero Express your result n lters ()What s the nal pressure o the gas? Express your result n atmospheres (a) pplyng the equaton o deal gas nr, the ntal absolute temperature o the gas s 8 (K) Rn 8 (b) he work done by the gas along the sobarc segment o the path s W 8 ( ) 87 (c) pplyng the equaton o deal gas nr, the temperature o the gas along the sotherm 8 s 76(K) Rn 8 (d) he work s negatve along the sothermal segment o the path (e) In order that the total work done by the gas s zero, we have 8 (atm) B Fg7 (lters)

6 W nr ln W So the nal volume o the gas s e W nr e (m ) 9(l) () pplyng the equaton o deal gas nr, the nal pressure o the gas s nr (a) 6(atm) 9 Suppose that a sample o gas expands rom to 8 m along the dagonal path n the dagram shown n Fg8 It s then compressed back to m along ether path or path ompute the net work done on the gas or the complete cycle n (kpa) each case ath he net work done on the gas s the area o the cycle on the dagram he area o the cycle along path s S ( ) ( 8) ath (m ) So the net work done on the gas along path s 6 8 W Fg8 he area o the cycle along path s S So the net work done on the gas along path s ( ) (8 ) W gas s taken around a closed cycle on a - dagram as ndcated n Fgure 9 (a) Fnd the total work W done by the gas (b) What s the change n the nternal energy o the gas? (c) What s the total heat transer to the gas n executng ths cycle? I the gas s taken around the cycle n the opposte 6 (atm) 6 Fg9 (lters)

7 drecton: (d) Fnd the total work done by the gas; (e) Fnd the change n the nternal energy o the gas; () Fnd the total heat transer to the gas n executng the cycle n ths drecton (a) he total work W done by the gas s W S (6 ) (6 ) 678 (b) he change n the nternal energy o the gas s U (c) pplyng the rst law o thermodynamcs: U + W and U, the total heat transer to the gas n executng ths cycle s W 678 (d) he total work W done by the gas s W W 678 (e) he change n the nternal energy o the gas s U () he total heat transer to the gas n executng the cycle n opposte drecton s W 678